No its not ... every business I know ceases to provide you business after a certain number of days of non-payment ... Cable companies turn off your cable, electric companies turn off your light, Your landlord evicts you etc etc.
If you're paying for hosting ... as long as I have your data backed up, I'm pretty sure I can stop hosting your site by removing your dns records from my system
If you provide two services (say, design and hosting) you can't hold one "hostage" for non-payment on the other (that's my understanding at least).
Take it to small claims court, or let it go.